Deformations of the Lie-Poisson sphere of a compact semisimple Lie algebra
type: Item
instance of: scholarly article
zbMATH Open document ID: 1318.53093
DOI: 10.1112/S0010437X13007689
author: Ioan Mǎrcuţ
published in: Compositio Mathematica
publication date: 2014-08-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1208.2298
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 17B63
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 17B08
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 70G45
zbMATH DE Number: 6333821
zbMATH Keywords: Lie Poisson structure
zbMATH Keywords: Casimir functions
MaRDI profile type: Publication
Wikidata QID: Q115256458
arXiv ID: 1208.2298
cites work: Integrability of Poisson brackets
cites work: Smooth functions invariant under the action of a compact Lie group
cites work: A classification of topologically stable Poisson structures on a compact oriented surface
cites work: Rigidity properties of compact Lie groups modulo maximal tori
cites work: Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
OpenAlex ID: W3102282829
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title: Deformations of the Lie-Poisson sphere of a compact semisimple Lie algebra
review text: This work gives a perfect classification of Poisson structures on a Lie Poisson sphere that arise from a compact semisimple Lie algebra. It turns out that all such Poisson structures are of the form \(f\pi\), where \(f\) is a Casimir function and \(\pi\) is the standard Lie Poisson form induced from the Lie algebra. Moreover, any two such Poisson structures are isomorphic if and only if the corresponding Casimir functions are gauge equivalent, i.e., only differ by an outer automorphism of the Lie algebra.
description: scientific article; zbMATH DE number 6333821